Once a staff has replied to a ticket and no response comes back from the client, there should be a provision in the system to automatically close the ticket without any input from staff.
the Pending Status mod has that. Check the 1.6 mods section of the forums or here: http://www.tmib.net/content/osticket-16-st-add-pending-status-and-autoclose-tickets-after-5-days(http://www.tmib.net/content/osticket-16-st-add-pending-status-and-autoclose-tickets-after-5-days)
this should be native to the system... please put in next release.